It's a bit sad that dogs aren't allowed in the park or on the playing fields, but the dog owners brought the ban on themselves because the irresponsible ones didn't clear up after their dogs. Too many football and rugby matches had to be stopped while dog poo as cleared from the pitch. Sometimes the poo wasn't discovered until someone fell in it. :(

Here we have dog parks - parks specifically designed so that dogs can run free and romp and play with each other. We even have a tiny dog park, so that tiny dogs can do that safely without harassment from the larger ones.

Otherwise, I think dogs are supposed to stay on-leash in the parks, and we have pretty strong norms nowadays about collecting dog poop as it's made.